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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 1997 Volume 245, Pages 80–106 (Mi znsl535)

This article is cited in 18 papers

Representations of the deformed oscillator algebra under different choices of generators

V. V. Borzova, E. V. Damaskinskyb, S. B. Egorovc

a St. Petersburg State University of Telecommunications
b Military Technical University
c State Technological Institute of St. Petersburg

Abstract: We discuss from unique position different variants of the commutation relations of the algebra of the $q$-deformed boson oscillator related to the different choices of generators. We consider the generalised form of the commutation relations which include as particular cases all of the most popular variants of such relations. By more or less standard way we describe the methods of construction and classification of the representations of the $q$-deformed oscillator algebra under different choices of generators. We also discuss the possibility of introduction the Hopf algebra structure in this algebra. The possibility of construction of the universal ${\mathscr R}$-matrix for considered algebra are also briefly discussed.

UDC: 517.9

Received: 08.10.1996


 English version:
Journal of Mathematical Sciences (New York), 2000, 100:2, 2061–2076

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